Experimental tests of String Theory

Edit: By the way, have a look at this: http://arxiv.org/find/all/1/all:+AND+kane+AND+kumar+acharya/0/1/0/all/0/1 a list of papers relevant to this topic.

This post is intended to dismiss some of the claims that “String Theory isn’t testable“;.  So, let’s first list out some of the claims we hear about the experimental testability of  String Theory, in random discussions,  on comments by trolls on tRF , and by the well-known crackpots, (dubbed “Smoit”, but I suggest “Woilin”):

• String Theory disagrees with well-known Physics!
• Ya, whatever, fine, but it agrees with everything, so that basically means that String Theory isn’t testable! It’s like, pseudo-science!
• Ok, ok, but it isn’t testable at today’s energy scales, alright? Ha!
• Well, fine, whatever, but it has been experimentally disproven!
• Ok, fine, WHATEVER, but it hasn’t been experimentally proven, at least, ok? Ha! How will you counter that?!

Ok, so let’s counter each of them.

String Theory does agree with well-known Physics.

It is a trivial excercise to show that String Theory agrees with General Relativity.

One starts with the beta functionals, which describe the breaking of conformal symmetry due to the presence of the Dilaton. To keep Conformal Symmetry, these functionals must be set to be 0.

The coupling of the string to the Dilaton Field is described by the following action integral:

${q_\Phi&space;}\ell&space;_P^2\int&space;{\Phi&space;R\sqrt&space;{&space;-&space;\det&space;{h_{\alpha&space;\beta&space;}}}&space;{\text{&space;}}{{\text{d}}^2}\xi&space;}$

To derive the beta functionals, one may do this in Riemann Normal Coordinates (see at Wikipedia or at the n(Cat)Lab).

The breakdown of conformal invariance would then be: \\\

$$\left\langle&space;{T_\alpha&space;^\alpha&space;}&space;\right\rangle&space;=&space;-&space;\frac{{\pi&space;T}}{{{c_0}}}{\left(&space;{{\beta&space;_{\mu&space;\nu&space;}}\left(&space;g&space;\right){h^{\alpha&space;\beta&space;}}{\partial&space;_\alpha&space;}{X^\mu&space;}{\partial&space;_\beta&space;}{X^\nu&space;}&space;+&space;i{\beta&space;_{\mu&space;\nu&space;}}\left(&space;F&space;\right){h^{\alpha&space;\beta&space;}}{\partial&space;_\alpha&space;}{X^\mu&space;}{\partial&space;_\beta&space;}{X^\nu&space;}&space;+&space;\frac{1}{2}\beta&space;\left(&space;\Phi&space;\right)R}&space;\right)_{\operatorname{elec}&space;\operatorname{tromagnetic}&space;{\text{&space;worldsheet}}}}$$

With the beta functionals given by:

$\begin{gathered}&space;{\beta&space;_{\mu&space;\nu&space;}}\left(&space;F&space;\right)&space;=&space;\frac{{\ell&space;_P^2}}{2}{\nabla&space;^\lambda&space;}{H_{\lambda&space;\mu&space;\nu&space;}}&space;\hfill&space;\\&space;\beta&space;\left(&space;\Phi&space;\right)&space;=&space;\ell&space;_P^2\left(&space;{&space;-&space;\frac{1}{2}{\nabla&space;_\mu&space;}{\nabla&space;_\nu&space;}\Phi&space;+&space;{\nabla&space;_\mu&space;}\Phi&space;{\nabla&space;^\mu&space;}\Phi&space;-&space;\frac{1}{{24}}{H_{\mu&space;\nu&space;\lambda&space;}}{H^{\mu&space;\nu&space;\lambda&space;}}}&space;\right)&space;\hfill&space;\\&space;{\beta&space;_{\mu&space;\nu&space;}}\left(&space;g&space;\right)&space;=&space;\ell&space;_P^2\left(&space;{{R_{\mu&space;\nu&space;}}&space;+&space;\ell&space;_P^2\frac{{\delta&space;\left(&space;{{R_{\mu&space;\nu&space;\rho&space;\sigma&space;}}{R^{\mu&space;\nu&space;\rho&space;\sigma&space;}}}&space;\right)}}{{\delta&space;{g_{\mu&space;\nu&space;}}}}&space;+&space;2{\nabla&space;_\mu&space;}{\nabla&space;_\nu&space;}\Phi&space;-&space;{H_{\mu&space;\nu&space;\lambda&space;\kappa&space;}}H_\nu&space;^{\lambda&space;\kappa&space;}}&space;\right)&space;\hfill&space;\\&space;\end{gathered}$

To impose conformal invariance, these beta functionals must vanish, as follows:

$\begin{gathered}&space;{\beta&space;_{\mu&space;\nu&space;}}\left(&space;g&space;\right)&space;=&space;\ell&space;_P^2\left(&space;{{R_{\mu&space;\nu&space;}}&space;+&space;2{\nabla&space;_\mu&space;}{\nabla&space;_\nu&space;}\Phi&space;-&space;{H_{\mu&space;\nu&space;\lambda&space;\kappa&space;}}H_\nu&space;^{\lambda&space;\kappa&space;}}&space;\right)&space;=&space;0&space;\hfill&space;\\&space;{\beta&space;_{\mu&space;\nu&space;}}\left(&space;F&space;\right)&space;=&space;\frac{{\ell&space;_P^2}}{2}{\nabla&space;^\lambda&space;}{H_{\lambda&space;\mu&space;\nu&space;}}&space;=&space;0&space;\hfill&space;\\&space;\beta&space;\left(&space;\Phi&space;\right)&space;=&space;\ell&space;_P^2\left(&space;{&space;-&space;\frac{1}{2}{\nabla&space;_\mu&space;}{\nabla&space;_\nu&space;}\Phi&space;+&space;{\nabla&space;_\mu&space;}\Phi&space;{\nabla&space;^\mu&space;}\Phi&space;-&space;\frac{1}{{24}}{H_{\mu&space;\nu&space;\lambda&space;}}{H^{\mu&space;\nu&space;\lambda&space;}}}&space;\right)&space;=&space;0&space;\hfill&space;\\&space;\end{gathered}$

These are the field equations for the graviton, dilaton, and photon fields respectively. Notice that they have a rather fundamental basis, conformal invariance. We need to focus on this one:

${\beta&space;_{\mu&space;\nu&space;}}\left(&space;g&space;\right)&space;=&space;\ell&space;_P^2\left(&space;{{R_{\mu&space;\nu&space;}}&space;+&space;2{\nabla&space;_\mu&space;}{\nabla&space;_\nu&space;}\Phi&space;-&space;{H_{\mu&space;\nu&space;\lambda&space;\kappa&space;}}H_\nu&space;^{\lambda&space;\kappa&space;}}&space;\right)&space;=&space;0$

This is obviously the field equation for gravity. Notice that I have removed one term on the way. This term is ${&space;+&space;\ell&space;_P^2\frac{{\delta&space;\left(&space;{{R_{\mu&space;\nu&space;\rho&space;\sigma&space;}}{R^{\mu&space;\nu&space;\rho&space;\sigma&space;}}}&space;\right)}}{{\delta&space;{g_{\mu&space;\nu&space;}}}}}$.This is because I have assumed that the Riemann Curvature Tensor is negligibly small.

I don;’t need to.

${\beta&space;_{\mu&space;\nu&space;}}\left(&space;g&space;\right)&space;=&space;\ell&space;_P^2\left(&space;{{R_{\mu&space;\nu&space;}}&space;+&space;\ell&space;_P^2\frac{{\delta&space;\left(&space;{{R_{\mu&space;\nu&space;\rho&space;\sigma&space;}}{R^{\mu&space;\nu&space;\rho&space;\sigma&space;}}}&space;\right)}}{{\delta&space;{g_{\mu&space;\nu&space;}}}}&space;+&space;2{\nabla&space;_\mu&space;}{\nabla&space;_\nu&space;}\Phi&space;-&space;{H_{\mu&space;\nu&space;\lambda&space;\kappa&space;}}H_\nu&space;^{\lambda&space;\kappa&space;}}&space;\right)&space;=&space;0$

However, in the limit of little gravity, and no dilaton, this becomes the ordinary vacuum Einstein Field Equation.

String Theory also agrees with the Minimal Supersymmetric Standard Model (MSSM) as shown by [1] (pdf  here).    Upon Supersymmetry breaking, this means that it also agrees with the Standard Model j.

String Theory is testable.

What does String Theory predict?

It predicts scattering amplitudes, caisimir energy, superpartners, gravitons, an infinitude of particles in a mass spectrum, gravitons, extra dimensions, AdS/CFT, and what not?  Talking about AdS/CFT, see this recent paper  by Raju and Papadogmias [2] (pdf here)   and this one by Papawdogmias and Raju [3] (pdf here).         This means the prediction of certain operators in the conformal boundary.

String Theory is testable at today’s energy scales.

Firstly, that isn’t a valid deleteion argument, as it  is still testable.

Secondly, the Supersymmetry-related predictions of String Theory just depend on a certain number of parameters, called the Supersymmetry breaking parameters. For an $\mathcal{N}=1$ supersymmetric string theory (like a $G\left(2&space;\right&space;)$ manifold compactification of M-Theory), it is in fact possible to test the effects of supersymmetry, because the supersymmetry breaking  energy parameter is low enough!.

String Theory has withstood experimental tests.

Huh, no. The only experimental result in contrary to the predictions of String Theory is probably [4] (PDF here). Other than this,  String Theory has in fact been supported by experimental predictions. Also, the experiment does not rule out compactification lengths smallernthan half a milimetre.

String Theory has had experimental verification repeatedly.

See this article at the Mathematics and Physics Wikia (Introduction to String Theory)  for the entire list.

Note that the 125 GeV Higgs actually serves as an experimental support for String Theory.

So basically, these criticisms of String Theory are just some ingeniously crafted Markov Chains, cooked up by a computer repairman at the Mathematics Department of the University of Columbia, aka the “Troll King“, and popularised by the popular media, such as “The Scientific American”, a magazine devoted to misleading laymen and making them even more unscientific.

3 thoughts on “Experimental tests of String Theory”

1. Haha this is very informative and funny, nice :-)!

2. Very interesting post, but I confess I find your list of claims by detractors of string theory to be a bit “strawman-ish.”

–“String Theory disagrees with well-known Physics!”

Obviously false, as the theory is designed to be a GUT that encompasses all results of current physics theories.

–“Ya, whatever, fine, but it agrees with everything, so that basically means that String Theory isn’t testable! It’s like, pseudo-science!”

One does not imply the other. Since any valid GUT would reproduce known results of current theories, the fact that string theory agrees with everything currently known is a feature not a bug. The trickier issue is the testability of predictions *outside* the realm of known physics results, on which more below.

–“Ok, ok, but it isn’t testable at today’s energy scales, alright? Ha!”

As a GUT, the theory must be testable at *all* energy levels; again, the trickier problem is that the “interesting” (i.e., new and unique) aspects of the theory aren’t testable at today’s energy scales.

–“Well, fine, whatever, but it has been experimentally disproven!”

Certainly not yet; but again, we run into the falsifiability issue when we try to discuss predictions of the theory beyond the scope of currently known physics experiments.

–“Ok, fine, WHATEVER, but it hasn’t been experimentally proven, at least, ok? Ha! How will you counter that?!”

Essentially an uninformed restatement of the prior claim; scientific theories rely on the ability to make predictions, and the ability to create testable hypotheses that can validate or invalidate those predictions. So far (to my knowledge anyway), string theory has not been disproven.

To my mind, the bigger issues regarding string theory are:

–Is it “unscientific” from the standpoint of fundamental falsifiability?
–Even if it is “scientific”, is it of any value?

To be considered a scientific theory, string theory must allow for the creation of testable hypotheses that are falsifiable. Since it’s a GUT, it’s certainly testable using current limits of experimental energies to confirm that, yes, it is able to reproduce the expected results of all current physical theories.

Of course, string theory implies certain things about the fundamental structure of matter, and therefore suggests hypotheses that could, *in principle*, at high enough energy scales, be tested for their validity.

But consider an extreme case of a theory that makes unique predictions at *really* large energy scales. If the energy scales (or any condition of any test) required to actually test a hypothesis are inconceivably large, even so large as to, say, require the resources of a Kardashev Type-II or -III civilization (or beyond), is the hypothesis still considered “testable”?

From my personal standpoint, I consider any hypothesis that can *in principle* be tested by an experiment, regardless of the required scale of that experiment, to be “scientific” (as opposed to faith-based theories such as creationism that establish unfalsifiable fundamental and immutable assumptions (“an invisible and undetectable Creator created everything in the Universe”) that underly the theory).

But others will disagree. Hence, the arguments about scientific vs. unscientific string theory.

As I said, I consider string theory to be “scientific”. But is it useful?

If you have a theory that can only reproduce currently known results, and has no practical predictive value, it’s reasonable to ask: of what value is the theory? It might be beautiful, elegant, self-consistent and clean–but not particularly useful.

And if the new/unique predictions that it makes can only be verified by experiments that cannot physically be conducted–ever, for the foreseeable future–it brings to mind such past philosophical discussions as “how many angels can dance on the head of pin?”

None of this discussion is meant in any way to detract from or devalue string theory or the work that has gone into it. It’s only meant to reframe the questions about the scientific validity and usefulness of string theory to further lively discussion and debate.